Suggesting that it was time for China to take over Asian Security, would be viewed with horror by most other SE.Asian countries. IMO they would view it as China taking back her historic control over these areas.
Equally relieving for these countries in the Pacific is the fact that American presence in the Pacific is preventing China from pursuing her strategy of declaring the second island chain as in her core interests.
Southeast Asian nations' fears are totally misplaced, and I think subtlety encouraged by the United States. This all goes back to the Domino Theory when the U.S. put the fear of God into the region about the spread of Communism. "The reds are coming!" warned American diplomats, "So be pro-active and get them before they get you." And they went after leftists hard in Thailand, Malaysia, Singapore, and Indonesia.
There is a lot of racism in the region against the Chinese because they have been more economically successful than other ethnic groups. They are like the Jews of Southeast Asia. There were race riots targeting Chinese in Malaysia in the 1960s and Indonesia are recently as the 1990s. The Vietnamese government pushed much of their Chinese minority out starting in 1979 in retaliation for the Sino-Vietnamese border war. Going back to the Malay Emergency in the 1950s and Suharto's quasi-genocide against Chinese leftists, there has long been an insidious association between Chinese people and communism.
China's foreign policy since 1949 has been extremely benign compared to any other world power in the last 60 years. This is the fundamental thing the "China threat" alarmists get wrong. No doubt Mao and the CCP were extremist in their domestic policy. They went all out in their commitment to developing a socialist state, breaking a lot of eggs to achieve the mythical omelet. But in foreign policy, China has been restrained. They stayed out of the Korean War until they felt directly threatened. If China was committed to spreading socialism it would have backed the DPRK from the beginning. In the 1950s there were some skirmishes around the two smalls islands held by the KMT near the Chinese coast, but never an invasion. They supported Vietnam during the Vietnam War, but never sent half a million troops like the U.S. did to prop up the South Vietnamese government. China even reduced its military support for North Vietnam after 1972.
China fought short border wars with Vietnam and India, but in both cases, China did not take territory and did not commit their full power. These were limited wars with limited objectives that had nothing to do with spreading socialism. China never sought to spread socialism outside its borders like the USSR did in the 1940s-70s. China has not have either a territorially expansionist foreign policy, nor an ideologically evangelical policy. China supported the Khmer Rouge in 1979, but that was more of a Great Game policy because the Khmer Rouge were a Chinese ally while Vietnam was a Soviet ally. Besides, the Khmer Rouge fell and China ultimately did nothing about it.
In conclusion the PRC has never had, and does not have, an expansionist, aggressive foreign policy. I'd like to see a tabulation of foreign military actions by the USSR/Russia, the USA, France, and Britain in the last 60 years. Even Spain and Portugal have had more foreign military actions than China. China's foreign policy is closer to that of Switzerland than the other members of the UN Security Council.
The U.S. and China can't let Southeast Asian nations' irrational fears govern their policy. So SEA nations scared of China. What are they going to do if the U.S.
did cede responsibility for Pacific security to China? Are SEA nations going to go to war with China? Refuse to trade with China? Engage in a hopeless arms race? Form a military alliance? No, those actions would be self-defeating. China's actions would soon earn them the begrudging trust of Southeast Asia. China would probably partner with countries, conduct join patrols, and share in intelligence. China has so much to gain by treating SEA nations well and so little to gain by pushing them around.